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General Cubic Interacting Vertex for Massless Integer Higher Spin Fields
High Energy Physics - Theory · Submitted 25 May 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.
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The abstract, sentence by sentence
We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities $s_1, s_2, s_3$. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities $s_1, s_2, s_3$. | contribution 0.98 | 0.96 | 0.30 | asserted 1.00 |
| s1 | Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. | gap 0.37 | 0.77 | 0.09 | asserted 1.00 |
| s2 | As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives. | result 0.89 | 0.95 | 0.64 | asserted 1.00 |
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The paper
Original abstract
We consider a massless higher spin field theory within the BRST approach and construct a general off-shell cubic vertex corresponding to irreducible higher spin fields of helicities $s_1, s_2, s_3$. Unlike the previous works on cubic vertices, which do not take into account of the trace constraints, we use the complete BRST operator, including the trace constraints that describe an irreducible representation with definite integer helicity. As a result, we generalize the cubic vertex found in [arXiv:1205.3131 [hep-th]] and calculate the new contributions to the vertex, which contain additional terms with a smaller number space-time derivatives of the fields as well as the terms without derivatives.
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References
How the literature uses it
18 arXiv papers cite this in 67 sentences
Papers citing it · 46 sentences without a confident label
Builds on it 4 papers
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In the present article, we have obtained an exact representation for the quantities $𝒵_j$, for $j≥1$, that constitute the non-multiplicative part of a general cubic vertex constructed in [ref] for massless completely symmetric fields of arbitrary integer helicities $s_1$, $s_2$, $s_3$ in a $d$-dimensional Minkowski spacetime.
Towards the structure of a cubic interaction vertex for massless integer higher spin fields · Conclusion · 0.86
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The procedure is realized in the framework of the BRST approach, developing our earlier results for cubic vertices for irreducible massless fields [ref] , [ref] to higher spin field theories with complete BRST operator, which includes all the constraints that determine an irreducible massless or massive higher spin representation on equal footing.
Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields · Conclusion · 0.97
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Here we will construct the general solution for the cubic vertices in following cases for interacting higher spin fields: with $k, k≥3$ massless; with one massive and $(k-1)$ massless of spins $s_1, s_2, ..., s_k$ earlier developed within BRST approach for $k=3$ in [ref] , [ref] .
BRST-BV approach for interacting higher spin fields · Solution of BRST-BV equations for Cubic Vertices · 0.97
Uses its method or tool 2 papers
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Research is realized with partial using the BRST approach with complete BRST operator, which (following the method [ref] , [ref] , [ref] see as well the results for the massless fields with two-component spinor indices in $4d$ flat space [ref] ) contains converted set of operator constraints forming a first-class gauge algebra.
BRST-BV approach for interacting higher spin fields · Introduction · 0.98
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We have used these results to study a deformation procedure in the approach with a complete BRST operator, along the lines of [ref] , so as to obtain an interacting theory, in particular, a system of generating equations ([ref]) for the cubic vertices of $3$ copies of initial Lagrangian formulations, with a respective set of constraints and oscillators.
Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces · Conclusion · 0.82
Compares with it 3 papers
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In contrast to the previously known results on cubic vertices, the study of [ref] does not impose on interacting fields any algebraic relations that do not follow from the least action principle.
Towards the structure of a cubic interaction vertex for massless integer higher spin fields · Introduction · 0.81
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We stress, that suggested BRST-BV approach with complete BRST operator due to the condition of homogeneity of the BRST-BV action dependence in generalized field-antifield vector should be evaluated as the less general method to find deformations of classical action. gauge transformations and gauge algebra as compared to the possibilities of BRST approach [ref] , [ref] .
BRST-BV approach for interacting higher spin fields · Conclusion · 0.94
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However, the corresponding BRST operator has a different structure than that in [ref] , and the derivation of a cubic vertex now requires a separate analysis.
Cubic interactions of d4 irreducible massless higher spin fields within BRST approach · Summary · 0.99
Cites it as background 8 papers
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Recently the cubic vertices for symmetric massless higher spin fields with integer spins were considered within the BRST approach for $d≥4$ [ref] in Minkowski space where the BRST charge takes into account all the constraints.
Cubic interactions of d4 irreducible massless higher spin fields within BRST approach · Introduction · 0.84
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Cubic vertices for massless fields, when the corresponding BRST charge describes irreducible representations of the Poincaré group were constructed in [ref] .] The building blocks for the cubic vertices are BRST invariant expressions, and any function of these expressions is a priori (i.e., if one is concerned only with cubic interactions) a valid cubic vertex.
BRST methods for constructing quartic actions for spinning black holes · Introduction · 0.80
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We refer to [ref] for an analysis of the corresponding quadratic actions for both massive and massless totally-symmetric fields, whereas the review [ref] also discusses the endeavours to introduce interactions in first-quantized BRST approach to higher-spin fields (see also [ref] and references therein). 4 pt
Ambient-space variational calculus for gauge fields on constant-curvature spacetimes · Introduction · 0.97
What it cites · 18 sentences without a confident label
Builds on 2 papers
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As the result, the general solution for the equation ([ref]) for cubic vertex has the form [equation] where the vertex $|V^M(3)⟩_(s)_3-2(j)_3$ was defined in Metsaev's paper [ref] but with modified forms $ℒ^(i)_k_i$, ([ref]) and $𝒵_j$ instead of $Z^j$ ([ref]) [equation] and is numerated by the natural parameter $k$ subject to the equations [equation] Here the quantity $𝒵_j$ is determined, e.g. for $j=1$ as follows [equation] For $j>1$ the expressions for $𝒵_j$ may be derived in the similar way.
BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields · General solution for cubic vertices · 0.96
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First, they include the different $Q^tot$- BRST closed forms $ℒ^(i)_k_i$, $i=1,2,3$, $k_i = 1, ..., s_i$ and $𝒵$ constructed from ones $L^(i)$, $Z$ known from [ref] , where $L^(i)$ are the linear in oscillators and $Z$ is cubic in oscillators, [equation] Here we have used the relations ([ref]), ([ref])–([ref]) below, $p^(i)_μ = -i∂^(i)_μ$ and [equation] Second, these operators involve the new two-, four- , ..., $[s_i /2]$ forms in powers of oscillators, corresponding to the trace operators [equation] First of all we have to check that the operators ([ref]) and ([ref]) are closed relatively operator $Q^tot$ which is extension of the BRST operator in works [ref] , [ref] by the operators responsible for the traces.
Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation · General solution for cubic vertices · 0.84
Compares with 1 paper
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As a result, admissible cubic vertices for irreducible fields may involve terms with less space-time derivatives in comparison with [ref] .
BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields · Conclusion · 0.92
Cites as background 13 papers
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The development of the BRST approach for calculating the cubic vertex was initiated by paper [ref] .
Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields · Introduction · 0.92
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The BRST approach to a Lagrangian description of various free higher spin field models in Minkowski and AdS spaces has been developed in numerous works (e.g., see [ref] , [ref] , [ref] and the review [ref] ).
Lagrangian formulation of the massless higher integer spin fields in the AdS background · Introduction · 1.00
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The BRST approach to a Lagrangian description of various free higher spin field models in Minkowski and AdS spaces has been developed in numerous works (e.g., see [ref] , [ref] , [ref] and the review [ref] ).
Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation · Introduction · 1.00
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